document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28567>Question 28567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the intercept method to find the equation of a straight line passing through (-3,0) and (0,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15564 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the intercept method to find the equation of a straight line passing through (-3,0) and (0,2)<BR>\n" );
document.write( "The intercept form of equation to a straight line is given by<BR>\n" );
document.write( "x/(a) +y/(b) = 1 -----(1)<BR>\n" );
document.write( "where a and b are the x-intercept and the y-intercept respectively<BR>\n" );
document.write( "The given points on the line are A(-3,0) and B(0,2)<BR>\n" );
document.write( "Observe that the y-coordinate of A is zero and hence A is a point on the x-axis<BR>\n" );
document.write( "and the x-coordinate of B is zero and hence B is a point on the y-axis<BR>\n" );
document.write( "A(-3,0) and B(0,2)means the line traverses through the first and third  quadrant via the second quadrant meeting the x-axis at A which is 3 units to the left of the origin and meeting the y-axis at B which is 2 units above the origin<BR>\n" );
document.write( "Therefore a = (-3) and b= 2<BR>\n" );
document.write( "Therefore (1) becomes<BR>\n" );
document.write( "x/(-3) +y/(2) = 1<BR>\n" );
document.write( "-x/3 +y/2 = 1<BR>\n" );
document.write( "Multiplying through out by 6(which is the lcm of 3 and 2)<BR>\n" );
document.write( "(-x)X2 +yX(3) = 1X6<BR>\n" );
document.write( "-2x+3y = 6<BR>\n" );
document.write( "That is 2x-3y = -6 (multiplying by (-1) through out)<BR>\n" );
document.write( "That is 2x-3y+6 = 0  ----(*)<BR>\n" );
document.write( "Verification: We check if A(-3,0) and B(0,2) hold in (*)<BR>\n" );
document.write( "Putting A in (*) that is putting x=-3 and y=0 in (*)<BR>\n" );
document.write( "LHS = 2x-3y+6  = 2X(-3)-3X(0)+6 = -6-0+6 = 0 =RHS<BR>\n" );
document.write( "Therefore A(-3,0) is a point on our line<BR>\n" );
document.write( "Putting B in (*) that is putting x=0 and y=2 in (*)<BR>\n" );
document.write( "LHS = 2x-3y+6  = 2X(0)-3X(2)+6 = 0-6+6 = 0 =RHS<BR>\n" );
document.write( "Therefore B(0,2) is a point on our line<BR>\n" );
document.write( "Therefore the equation: 2x-3y+6 = 0  is correct\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );